Answer:
The probability that on a given day below 6,214,323 drinks are sold is 0.8413.
Step-by-step explanation:
The provided information are:
Population mean [tex](\mu)[/tex] = 6,205,195
Population standard deviation [tex](\sigma)[/tex] = 9,120.32
Consider, X be the random variable that represents the number of drinks that are sold on a given that is normally distributed with the mean = 6,205,195 and standard deviation = 9,120.32.
The probability that on a given day below 6,214,323 drinks are sold can be calculated as:
[tex]P(X<6,214,323) = P(\frac{X-\mu}{\sigma} < \frac{6,214,323-\mu}{\sigma} )\\P(X<6,214,323) = P(Z < \frac{6,214,323-6205195}{9120.32} )\\P(X<6,214,323) = P( Z < 1.0008)\\P(X<6,214,323) = 0.8413[/tex]
It must be noted that P(Z < 1.0008) = 0.8413 has been calculated using the standard normal table.
Hence, the required probability is 0.8413.
